- không là ko

- ừ là uk

- mình là mk

- thank you là tk

- bạn là bn

- câu lạc bộ là CLB

- ủy ban nhân dân là UBND

- trung học cơ sở là THCS

Ví dụ : nước là nc

Đang là dg , không là ko , ...

\(S=1\cdot2+2\cdot3+3\cdot4+...+2011\cdot2012\)

\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+2011\cdot2012\cdot3\)

\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+2011\cdot2012\cdot\left(2013-2010\right)\)

\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...+2011\cdot2012\cdot2013-2010\cdot20112012\)

\(\Rightarrow3S=2011\cdot2012\cdot2013\)

\(\Rightarrow S=\frac{2011\cdot2012\cdot2013}{3}\)

1/2x=5/12+2/3

1/2x=13/12

x=13/12:1/2

x=6/13

Vậy x  = 6/13

\(0,5-\frac{2}{3}x=\frac{5}{12}\)

\(=\frac{1}{2}x=\frac{5}{12}+\frac{2}{3}\)

\(=\frac{1}{2}x=\frac{13}{12}\)

\(\Rightarrow x=\frac{13}{12}:\frac{1}{2}\)

\(\Rightarrow x=\frac{6}{13}\)

Vậy x = \(\frac{6}{13}\)

(#)

:3

Ta có : 

\(\frac{4.5}{2.15}=\frac{2.1}{1.3}=\frac{2}{3}\)

Tham khảo nha !!! 

Đặt \(A=4+2^2+2^3+2^4+...+2^{60}\)

\(A=2^2+2^2+2^3+...+2^{60}\)

\(2A=2^3+2^3+2^4+...+2^{61}\)

\(2A-A=\left(2^3+2^3+2^4+...+2^{61}\right)-\left(2^2+2^2+2^3+...+2^{60}\right)\)

\(A=2^3+2^{61}-2^2-2^2\)

\(A=2^3+2^{61}-2^2\left(1+1\right)\)

\(A=2^3+2^{61}-2^2.2\)

\(A=2^3+2^{61}-2^3\)

\(A=2^{61}\)

Vậy \(A=2^{61}\)

Chúc bạn học tốt ~ 

Gọi ƯCLN\(\left(2n+3;3n+7\right)=d\)

\(\Rightarrow\orbr{\begin{cases}2n+3⋮d\Rightarrow3.\left(2n+3\right)⋮d\Rightarrow6n+9⋮d\\3n+7⋮d\Rightarrow2.\left(3n+7\right)⋮d\Rightarrow6n+14⋮d̸\end{cases}}\)

\(\Rightarrow\left(6n+14\right)-\left(6n+9\right)⋮d\)

\(\Rightarrow5⋮d\Rightarrow d\in1;5\)

\(+d=5\Rightarrow6n+9⋮5\Rightarrow5n+\left(n+9\right)⋮5\)

\(\Rightarrow n+9⋮5\Rightarrow n+4⋮5\Rightarrow n=5k-4\)

Vậy n=5k-4 thì rút gọn đc

Vậy \(n\ne5k-4\Rightarrowđpcm\)

* Cách 1 : 

Ta có : 

\(16A=\frac{4^{17}+16}{4^{17}+1}=\frac{4^{17}+1+15}{4^{17}+1}=\frac{4^{17}+1}{4^{17}+1}+\frac{15}{4^{17}+1}=1+\frac{15}{4^{17}+1}\)

\(16B=\frac{4^{14}+16}{4^{14}+1}=\frac{4^{14}+1+15}{4^{14}+1}=\frac{4^{14}+1}{4^{14}+1}+\frac{15}{4^{14}+1}=1+\frac{15}{4^{14}+1}\)

Vì \(\frac{15}{4^{17}+1}< \frac{15}{4^{14}+1}\) nên \(1+\frac{15}{4^{17}+1}< 1+\frac{15}{4^{14}+1}\)

\(\Rightarrow\)\(16A< 16B\) hay \(A< B\)

Vậy \(A< B\)

Chúc bạn học tốt ~ 

\(4^2.A=\frac{4^2\left(4^{15}+1\right)}{4^{17}+1}\); \(4^2.B=\frac{4^2\left(4^{12}+1\right)}{4^{14}+1}\)

=> \(4^2.A=\frac{4^{17}+4^2}{4^{17}+1}\);\(4^2.B=\frac{4^{14}+4^2}{4^{14}+1}\)

=> \(4^2.A=\frac{4^{17}+1+4^2-1}{4^{17}+1}\); \(4^2.B=\frac{4^{14}+1+4^2-1}{4^{14}+1}\)

=> \(4^2.A=\frac{4^{17}+1}{4^{17}+1}+\frac{4^2-1}{4^{17}+1}\); \(4^2.B=\frac{4^{14}+1}{4^{14}+1}+\frac{4^2-1}{4^{14}+1}\)

=> \(4^2.A=1+\frac{4^2-1}{4^{17}+1}\); \(4^2.B=1+\frac{4^2-1}{4^{14}+1}\)

Mà \(4^{17}>4^{14}\)

=> \(4^{17}+1>4^{14}+1\)

=> \(\frac{4^2-1}{4^{17}+1}< \frac{4^2-1}{4^{14}+1}\)

=> \(1+\frac{4^2-1}{4^{17}+1}< 1+\frac{4^2-1}{4^{14}+1}\)

=> \(4^2.A< 4^2.B\)

=> \(A< B\)

\(\frac{x-1}{2}=\frac{x+2}{4}\) <=> \(x-1=\frac{x+2}{2}\)

<=> 2x-2=x+2  <=> 2x-x=2+2  => x=4

Đáp số: x=4

\(=\frac{2\left(x-1\right)}{4}=\frac{x+2}{4}\)

\(=\frac{2\left(x-1\right)\cdot4}{4}=\frac{\left(x+2\right)\cdot4}{4}\)

\(=2\left(x-1\right)=x+2\)

\(=2x-2=x+2\)

\(=2x-x=2+2\)

\(=x=4\)

<=> 2xy-x=4y+4

<=> x(2y-1) = 4y+4  => \(x=\frac{4y+4}{2y-1}=\frac{4y-2+6}{2y-1}=\frac{2\left(2y-1\right)}{2y-1}+\frac{6}{2y-1}\)=> \(x=2+\frac{6}{2y-1}\)

Để x nguyên => 6 chia hết cho 2y-1  => 2y-1=(-6,-3,-2,-1,1,2,3,6)  => y=(-5/2; -1; -1/2; 0; 1; 3/2; 2; 7/2)

Do y nguyên nên ta chọn được y=(-1, 0, 1, 2) => x=(0, -4, 8, 4)

Các cặp (x,y) thỏa mãn là: (0; -1), (-4,0); (8,1); (4,2)